2C+Logarithms

How do we use Logarithms?
We use logarithms in the case where we know what a number raised to a power equals, but we do not know what power that number was raised to.

math 3^x=729 math

math x=WTF!? math

To use logarithms we harness the term "log" in which case if we wanted to know the logarithm of 3 to the x power, we would simply input a "log" in front of the 3 to the x power.

math 3^x math

math Log3^x math

However in an equation like 3 to the x power equals 729, we would do the logarithm of 3 to the x power and 729.

math 3^x=729 math

math Log3^x=Log729 math

Once we take the Log of 3 to the x power, we bring down the x as a coefficient. We could do the same for Log of 729, but it would be a waste of time because 729 is raised to the 1st power, and 1 times any number equals the number itself.

math 3^x=729 math

math Log3^x=Log729 math

math xLog3=1Log729 math

math xLog3=Log729 math

Then once we've accomplished that we divide each side by Log of 3 to discover what x equals.

math 3^x=729 math

math Log3^x=Log729 math

math xLog3=1Log729 math

math xLog3=Log729 math

math x=\frac{Log729}{Log3} math

math x=6 math

Another Example of Usage of Logarithms

math 5^x=9765625 math

math Log5^x=Log9765625 math

math xLog5=Log9765625 math

math x=\frac{Log9765625}{Log5} math

math x=10 math

What exactly are Logarithms?
A logarithm is the opposite, more commonly known as inverse, of exponents. The general equation associated with logarithms is:

math log_bn=m math

Which translates into:

math b^m=n math

When graphing a logarithm, the b must always equal 10. If there is no number registered for "b" in a logarithm formula, then we assume that b=10. However we use b^m=n when b is any number but 10.

To make b^m=n into a graphing form, when b does not equal 10, we:

math log_bn=m math

math b^m=n math

math Logb^m=Logn math

math mLogb=Logn math

math m=\frac{Logn}{Logb} math

Naima Holland FX-63 a. 2(x+3)=64 64=2x2x2x2x2x2 64=26 2(x+3)=26 x+3=6 subtract 3 from both sides. x=3 b.8x=46 8=2x2x2x2 8x=(23)x=23x 4=2x2 46=(22)6=212 23x=1212 3x=12 divide 3 by both sides x=4
 * 10

c.9x=1/27 9=3x3 9x=(32)x=32x 27=3x3x3 1/27=1/33=3-3 32x=3-3 2x=-3 divide each side by 2 x=-1.5 or =3/2

Problem Topic: Solving equations and logarithms Notes: The first type of logarithmic equation has two logs, each having the same base, set equal to each other, and you solve by setting the insides (the "arguments") equal to each other.